How to Stay Solvent Longer Than the Market Can Stay Irrational

How often have you heard the quip, "The market can stay irrational longer than you can stay solvent"? The idea: Even if the market is ridiculously overvalued, you won't make money by shorting it. You'll probably go bankrupt instead of laughing all the way to the bank.

But isn't the obvious solution to this problem simply to repeatedly sell a smaller amount short?

Suppose for example that you've got $100,000 in assets. You know with virtual certainty that the market will eventually fall from its present level of 100 down to its fundamental value of 50. The catch: You don't know when it will fall. Every year, the market has a 50% of going up 20%, and a 50% chance of plummeting down to 50. So if you sell $100,000 short with contracts that resolve after a year, you'll lose your shirt if the market goes up five years in a row.

However, you could easily just sell $10,000 short each year. In year one, you lose $2,000 if the market goes up to 120, and make $5000 if the market falls back to 50. In year two, you lose $2,000 if the market goes up to 144, and gain $5833 if it falls back to 50. In year three, you lose $2000 if the market goes up another 20%, and gain $6528 if it falls back to 50. Every year you can expect to make money, and unless you're wrong 50 times in a row, you stay solvent.

Did I cook the numbers to make this work? I don't think so. The strategy won't work if the ex ante payoff from short-selling is negative. If the market has a 50% chance of doubling and a 50% chance of falling to its fundamental level, you quickly go broke. But under realistic assumptions, what's wrong with my strategy?

The problem is that bubbles are irrational. Just when you think the top is in, the security runs and runs. In your example, your 5 year figure will be wrong by 10 years. It takes 15 years to get back to 50, and you are out of the market or became bullish by year 7 or 8.

The real problem with this approach is margin. If your short position pops, you will need to use some of that assumed principal to cover the unrealized loss in your short (not double down), so that your broker or clearing exchange will allow you to put on an even bigger position.

Under Reg T, you need 150% of the short position you want to take, at the time you want to take it. So in the example above, if you've got $5,000 in your account and you put on a $10,000 short position, and the position is $2,000 underwater, you need to allocate another $7,000 in your account to put on another $10,000 short. In addition to paying margin interest.

There can be other issues, such as locate issues, so you are bought in because the party who loaned you the shares to short (even in ETFs, occasionally) wants them back. You probably know better than me the negative convexity aspects of a callable asset.

First, you assume that it goes back to 50, rather than a -50% decline. In practice, I would believe that the fundamental value would increase over time so that a -50% decline is more reasonable than a return to 50. Hence you give yourself a greater return on the short side than is probably likely.

Second, you are selling short a fixed amount of money, rather than a fixed percentage of your portfolio. This means you are not operating a martingale strategy. Under your strategy, the more your portfolio declines, the more you are willing to bet (as a percent of assets) that you there will be a correction. Since probabilities are binomial, the probability of getting a correction given that you haven't had one yet after 4-5 years goes very high. The real world market is not necessarily like that.

Basically, the returns are going to be good the way you set up the problem.

Not satisfied with a line a wrote. I know the events are independent so that in each period it is a 50% probability, but as the number of years increases, the probability that at least one of them will have a correction increases very sharply.

"John Hall" (a real name? :-) stated the things rather clearly. My addition is a general remark: yes, if you are more prudent, you are more likely to outlast the market's irrationality, but, OTOH, noone got famous for eking out a 5% return (your total capital is $100k, and if you are right the first year, your stated profit is $5k).

They only pay off with the price of the stock at some future date but you don't get the dividends.

So you can buy a stock and short the future and you get the dividends. Of course you pay for this and the difference in the spot price and the futures contract is the discounted expected value of the dividends.

I think the futures market is pretty light, so if you can't short your individual stock you can short the S&P index, but then you have basis risk.

In general I think the "The market can stay irrational longer than you can stay solvent" critique is way over stated. There are tons of ways to short the market without blowing up.

The first and easiest is to move your current stocks into cash. You can hold that position forever.

You can also hold $100 in cash and short futures such that the market would have to go to zero before your capital was eaten up by margin calls. You can't get knocked out of that position either. The key is to avoid big leverage.

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